Yoho International youth hostel is quite easily The Best hostel I've stayed at so far in Europe, as well as The Only hostel you should consider staying at when in lovely Salzburg. Yoho is one of those hostels that's the perfect size: not so big that it's impossible to meet anyone; and not so small that there's nobody there to meet. The bar is open every night, it's there to be visited, and visit it is what everyone does. Yoho is also famous for playing "The Sound of Music" in their TV room, every single day at 10:30am — if you're crazy enough to want to watch it while you're there, then feel free. I think the hostel's slogan says it all: "easy to find, hard to leave".
Rooms: spacious, clean and secure — and plenty of them. By the way: if HostelWorld et al tell you that there are no beds available, don't believe it: contact Yoho directly to hear the full story. I was unable to book all my time here in advance on HostelWorld: but when I arrived, I found that they easily had space for all the nights that I wanted.
People: really friendly backpacker bunch, willing to explore the town with you by day, or to have a beer with you by night.
Staff: some of the friendliest I've seen in a European hostel.
Location: 5-minute walk from the train station, and 10-minute walk from most of the sights of central Salzburg. Salzburg's not a very big place: everything's an easy walk away.
Food: the breakfast menu is extensive but pricey; however, the cereal and tea/coffee is sitting on the counter, and you can generally get away with helping yourself for free. They also serve dinner every night, at very good prices and of good quality.
Internet: yet another "€2/hr in the hostel, €1/hr round the corner" affair.
Hot water: pretty good, although the bathrooms are a little dodgy.